Question

Suppose a homeless shelter provides meals and sleeping cots to those in need. A rectangular cot measures 6 feet long by 3 ½ feet wide. Find the cot's diagonal distance from corner to corner. Round your answer to the nearest hundredth foot. 6.95 feet 9.64 feet 9.65 feet 6.94 feet

Answer 1

Answer:

6.95 feet

Step-by-step explanation:

The shape of the cot is rectangular. A diagonal of the rectangle divides the rectangle into two Congruent Right Angled triangles. The length and width of the rectangle become the legs of the right triangle and the diagonal is the hypotenuse of the right triangle.

In order to find the length of the hypotenuse which is the diagonal in this case we can use the Pythagoras Theorem. According to the theorem, square of hypotenuse is equal to the sum of square of its legs. So for the given case, the formula will be:

$\textrm{(Diagonal)}^{2}=\textrm{(Length)}^{2}+\textrm{(Width)}^{2}\\\\ \textrm{(Diagonal)}^{2}=6^{2}+3.5^{2}\\\\ \textrm{(Diagonal)}^{2}=48.25\\\\ \textrm{(Diagonal)}=\sqrt{48.25}=6.95$

Thus, rounded of to nearest hundredth foot, the diagonal distance from corner to corner is 6.95 feet